Bath had not led until the 65th minute but even when home lock James Percival responded by crashing over for the only try of the game soon after, it was the accuracy of Barkley that proved decisive.
By contrast Andy Goode spurned a couple of kicks late on, including failing to convert Percival's 69th-minute score, which proved crucial when his opposite number landed the winning blow with the final kick of the game.
Worcester had raced out to a 12-0 with Goode initially solid with the boot as he slotted a 40-metre penalty in just the second minute.
Minutes later Bath offended in the ruck area and again the outside half was on target, this time from 35 metres.
The Warriors continued to dominate play and when Matt Banahan was penalised for not rolling away at a ruck, Goode converted his third penalty to give his side a 9-0 lead after only 10 minutes.
Worse was to follow for Banahan and Bath. The centre was yellow carded for a deliberate knock on and again Goode made no mistake with his penalty kick.
Banahan was soon joined in the sin-bin by rival captains, Stewart Hooper and Dean Schofield, who were yellow carded by young referee, Luke Pearce, after a substantial melee involving most of the forwards.
However, the Warriors failed to take advantage of their numerical superiority.
Barkley reduced the arrears with the first of his eight penalties and Banahan then returned with no damage done to his side's chances.
Goode should have restored Worcester's 12-point advantage but the outside half fired wide with a 30-metre drop-kick attempt.
Another error from the Warriors saw Josh Drauniniu fail to collect an up-and-under and another penalty was conceded for offside which Barkley kicked from 45 metres.
A simple penalty from Goode after 32 minutes made it 15-6 to the Warriors and they should have extended that lead when they blew the best try scoring opportunity of the half.
Goode, David Lemi and Josh Matavesi combined brilliantly in a sweeping 70-metre move but Lemi's scoring pass to Goode was ruled forward.
Bath scored the first points of the second half when Barkley was successful with a 45-metre penalty and the lead was soon down to three points with another simple goal from the outside half.
A handling error from Lemi and a powerful run from Banahan exerted more pressure on the Warriors defence and they conceded another penalty at the ruck area to allow Barkley to tie up the scores.
Bath were now the dominant side with Banahan becoming increasingly influential with his driving runs in midfield and they looked the more likely winners as the game entered the final quarter.
Barkley gave Bath the lead for the first time in the match with a 35-metre penalty after 65 minutes.
Stung by the reverse Worcester immediately brought on three replacements and it soon paid dividends when Percival drove over from close range but Goode's conversion rebounded back of a post which proved costly as Barkley was successful with his longest penalty of the game to give Bath a one-point lead with six minutes remaining.
Back came the Warriors to secure two penalties in the Bath 22, Goode surprisingly missed the first but kept his nerve to kick the second.
But with the last kick of the match Barkley made no mistake with his eighth penalty and with it an away victory.
Elsewhere, Exeter Chiefs' convincing 43-6 victory over Sale Sharks at Sandy Park means that the Devon side not only recorded their biggest ever league win but have also won their opening day match on each of their three seasons in the Premiership.
The Chiefs took a try-scoring bonus point as they crossed for six tries, two of them from Matthew Jess, as they restricted the visitors to just two penalties to remain unbeaten in five games against the Sharks.
Former England fly-half Danny Cipriani had to bide his time on the Sale replacements bench to mark his return to the Premiership after two seasons with Melbourne Rebels.
Just after the half-hour mark, Cipriani took to the field and slotted in to the fly-half berth with Nick MacLeod switching to inside centre as Sam Tuitupou limped out of the game.
Sale Sharks new boss Bryan Redpath gave club debuts to wing Corne Uys (Newcastle Falcons) and lock Richie Gray (Glasgow) but MacLeod started at fly-half.
Scotland head coach Andy Robinson was at the game to watch Gray, who was his outstanding player in last season's Six Nations, as he prepares for the Autumn internationals against New Zealand, South Africa and Tonga.
Even though Exeter Chiefs had made eight signings during the summer but head coach Rob Baxter gave debuts to just two - centre Ian Whitten and scrum-half Will Chudley.
Despite various pre-season games both sides took time to settle in to their game and the Chiefs had problems in both the scrum and Chris Whitehead's lineout throws.
But it was the home side who put the first points on the board through a 45-metre penalty from out wide from the boot of Argentina fly-half Ignacio Mieres after 12 minutes.
Mieres was on hand to score the Chiefs' first try of the Premiership season as he crossed the line after an excellent break up the middle from wing Josh Tatupu before off loading to James Scaysbrook.
The blindside flanker was stopped five metres short but from the second phase play, Whitten put Mieres over. His conversion attempt, though, hit the far upright and bounced the wrong way.
Mieres made amends with a second 45-metre penalty midway through the half but five minutes later MacLeod cancelled that out with the Sharks' first points of the game.
The Chiefs had the chance of a second try before the break after a run by Shoemark but with two players outside, he stepped inside and the ball was knocked on. Sharks were penalised at the scrum and Mieres landed his third penalty to give his side a 14-3 interval lead.
Exeter made the perfect start to the second half with number eight Richard Baxter making the lineout ball and lock Aly Muldowney crossing for the Chiefs' second try.
Mieres added the simple conversion before MacLeod landed his second penalty. But the Chiefs replied with Shoemark breaking down the left before giving the scoring pass to Jess to cross for the third try.
Midway through the second period the Chiefs scored their bonus-point try starting from a Mieres break before who linked-up with Tatupu to put flanker Tom Johnson through for the touchdown.
Replacement scrum-half Kevin Barrett then picked up from the back of the scrum and flipped the ball out of the back of his hand to set up an overlap, with Jess racing down the touchline for his second try of the day.
With less than 10 minutes to go local hero Chris Budgen, who had been on the field less than 10 minutes, had his hand on the ball at the bottom of the pack for a try to which Gareth Steenson added the extras.
And Northampton held on with just 13 men to beat Gloucester 24-19 in a thrilling finale at Kingsholm.
The Saints scored three tries to one, with centre George Pisi getting two of them and England cap Dylan Hartley the other.
Fly-half Ryan Lamb landed a penalty and three conversions.
A penalty try for Gloucester along with four penalties and a conversion from Freddie Burns just was not enough for the home side.
Former England captain Mike Tindall, who is combining his playing career at Gloucester with learning the coaching ropes, formed a new centre partnership with ex-Leicester midfield man Billy Twelvetrees.
The former Tigers youngster was one of five players in the Cherry and Whites 22 making their debuts, with England back-row Ben Morgan at number eight.
Northampton had five players starting a Premiership match for the first time, with Samoan wing Ken Pisi joining his brother George in the backs, centre Dominic Waldouck in the team and South African number eight Gerrit-Jan van Velze starting in the back row.
Anticipation before kick-off was for a close game game as the sides had run each other to the wire twice last season.
The opening exchanges were fierce in this latest encounter. But Northampton soon found a key weakness in the home armour on the left wing and exploited it.
The Saints pack went around the blindside to drive close early on but, after a short attack by the Cherry and Whites, Northampton found the tryline as Hartley put Pisi away on the left and the centre cut inside to cross.
Again, they almost went in on the left before Hartley took a pass from the base of a ruck to dive in at the corner, with Lamb booting his second conversion.
Gloucester finally got on the board when Burns landed a 30-metre penalty but the Cherry and Whites needed to get a spark from somewhere to get them going.
A second Burns penalty shortly before the break reduced the arrears briefly before Lamb kicked his first penalty to restore the 11-point advantage at half-time and give new home coach Nigel Davies a lot to talk through in the dressing room.
Gloucester hit back with two Burns penalties as they clawed their way back into the game but they needed tries but it was Northampton who were scoring them as Pisi went over again on 50 minutes after a move across the backs to the right where prop Soane Tonga'uiha gave him the scoring pass.
Burns had the home fans on their feet when he intercepted a loose pass in his own 22 and raced upfield but did not have the support to make the chance count and then a neat chip over the Saints defence gave replacement Huia Edmonds a chance but he could not get the ball grounded over the line.
Gloucester needed two tries and a conversion to draw and had a chance for one of them when van Velze and then prop Paul Doran-Jones were sin-binned.
It left the Saints pack seriously depleted as they gave away a penalty try for collapsing a scrum. Northampton's 13 men were under the cosh back in their own half but full-back Jonny May dropped a chance with the line in front of him.
The home side had one final chance to grab the winning try but a knock-on from replacement centre Henry Trinder finished Gloucester's hopes.
- Andy Goode
- Matt Banahan